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Fishery Bulletin 93(1), 1995 



Growth in length data were analyzed by using 

 FISHPARM, an IBM PC compatible program (Prager 

 et al., 1987), which implements Marquardt's algo- 

 rithm for nonlinear least squares parameter estima- 

 tion (Marquardt, 1963). 



Bernard's (1981) multivariate analysis for compar- 

 ing growth curves was employed to test the hypoth- 

 esis that male and female vertebral growth curves 

 were the same. This method also determines which 

 of the von Bertalanffy parameters are the most sta- 

 tistically significant cause of any differences in 

 growth. 



Marginal increment analysis 



Validation, the confirmation of the temporal mean- 

 ing of the growth increment (Brothers, 1983), is dif- 

 ficult to attain for large pelagic species and was at- 

 tempted by using marginal increment analysis. The 

 marginal increment ratio (MIR) (Skomal, 1990) was 

 calculated by using the following equation: 



MIR = (VR - R n )/(R„ - R n ^), 



where VR = the vertebral radius; 



R n = the last complete band; and 

 R n _ 1 = the next to last complete band. 



Mean MIR was plotted against month to locate peri- 

 odic trends in band formation. The MIR relates the 

 edge formation to the width of the previous completed 

 band, which corrects for differences in band width 

 between small and large fish. 



Length frequency 



Length-frequency distributions were analyzed by us- 

 ing Shepherd's (1987) model. The sample was sepa- 

 rated by sex and calculations were made at 3-cm in- 

 tervals. Initial values of L m and K, based on biologi- 

 cal parameters obtained from the literature (Springer, 

 1960; Compagno, 1984) were entered into the pro- 

 gram which was then rerun until the highest score 

 function was attained. The L M and if associated with 

 this score function were used to calculate t Q by using 

 the following equation: 



t Q = t + (UK) (\n[L x - L t ]/LJ, 



where t = (birth); 



L t = mean size at birth; 



K = the von Bertalanffy growth constant; 



and 

 L oo = the mean asymptotic fork length. 



Longevity 



Estimates of longevity were obtained by using tag 

 and recapture data. Data on eight recaptured dusky 

 sharks at liberty for greater than 10 years were ex- 

 amined. Age at tagging was assigned from the size 

 estimate provided at the time of release. This esti- 

 mated age was based on growth curves derived from 

 vertebrae. The number of years at liberty were then 

 added to estimate age at recapture. 



Results 



Vertebral samples 



Of the 171 processed vertebra, 36 (21.0%) were con- 

 sidered unreadable. Initial agreement by two or more 

 readers was reached on 89 specimens. The remain- 

 ing 50 sections were recounted by two of the investi- 

 gators. A consensus was reached on 37 of those re- 

 counted and the rest were discarded as unreadable. 

 Six were then eliminated for having no information 

 on sex. The remaining 120 (70.2%) consisted of 53 

 male and 67 female specimens ranging in size from 

 a 73 cm FL neonate to a 296 cm FL adult female. 

 The FL-VR regression showed a linear relationship: 



FL = 12.82(VR) + 24.99 [n = 114; r 2 = 0.99] . 



The FL to VR relationship was significantly differ- 

 ent between the sexes for all fish combined 

 (ANCOVA, P<0.05). However, this was due to three 

 large females whose removal from the analysis al- 

 tered the curves and showed the males and females 

 to be statistically indistinguishable (P<0.05) (Fig. 1). 

 We chose to use the combined relationship without 

 those three samples. 



Back-calculated as compared with empirical 

 length-at-age data show a smaller estimated size for 

 fish of younger ages, when calculated from the ver- 

 tebrae of the older fish, indicating the presence of a 

 slight Lee's phenomenon for both sexes (Table 1). 

 Lee's phenomenon was more pronounced in females 

 and increased with age. 



The MIR data showed a distinct, periodic trend of 

 increasing increment growth from April through 

 June (female) or July (male); after this peak there 

 was a slight decrease and apparent leveling (Fig. 2). 

 The decrease in incremental growth is not large 

 enough to indicate a double band formation. The 

 graph suggests that an annual winter band is formed 

 between September and April. This band can be vis- 

 ible by February in males; no data were available 

 for females. The time of annulus formation cannot 



